Ahead of their clash at Aston Villa tomorrow night, Slot also revealed Cody Gakpo is out of the trip.
Gomez suffered a hamstring injury in their FA Cup defeat at Plymouth Argyle and will now go under the knife.
“I think both are not available for tomorrow,” Slot said this morning. “Cody is close to being back and Joe will take quite a long time.
“He is going to be out for a number of weeks because of a hamstring injury. It was a big blow for us and for him.
“He tried to do everything to be with the team. He worked really hard to come back, then first game when he came back, after two or three minutes we saw him making a sprint and now he's out for weeks again.
"It's always very hard for a player in every part of the season, let alone in the part of the season that everybody is looking forward to.”
Slot added on Gomez, "He will miss large parts of the end of the season.
“But we expect him to be back in the end phase of the season. He might need surgery but that's something we still have to assess.”